Pilot assignment in cell free massive MIMO wireless systems

ABSTRACT

Systems and methods for assigning pilot sequences include randomly assigning pilot sequences to a population of access terminals. A first pilot sequence assigned to a worst performing access terminal of the population of access terminals is updated to a different pilot sequence that improves performance of the worst performing access terminal. A second pilot sequence assigned to a best performing access terminal of the population of access terminals is updated to another pilot sequence that reduces performance of the best performing access terminal.

BACKGROUND OF THE INVENTION

The present invention relates generally to wireless communicationsystems and more particularly to pilot sequence assignment in a cellfree massive multiple-input multiple-output wireless system.

In a cell-free wireless communications system, access terminals areserviced by access points. In accordance with time division duplex (TDD)protocols, the access terminals synchronously and simultaneouslytransmit their pilot sequences to all access points. Each access pointuses the pilot sequences to estimate channel coefficients between itselfand each access terminal. High throughput in such a wirelesscommunications system is achieved due to these estimated channelcoefficients. The best estimates of channel coefficients can be obtainedif the pilot sequences are orthogonal. Unfortunately, when the number ofaccess terminals is large, the length of the pilot sequences must beincreased to maintain orthogonality. However, the time required for longpilot sequences may be too long due to the limited length of thecoherence interval. As such, short (and therefore non-orthogonal) pilotsequences are assigned to the access terminals. Current solutions forassigning non-orthogonal pilot sequences to access terminals result in arelatively low level of performance as compared to the ideal case whenall pilot sequences are orthogonal.

BRIEF SUMMARY OF THE INVENTION

In accordance with one embodiment, systems and methods for assigningpilot sequences include assigning pilot sequences to a population ofaccess terminals. A first pilot sequence assigned to a worst performingaccess terminal of the population of access terminals is updated to adifferent pilot sequence that improves performance of the worstperforming access terminal. A second pilot sequence assigned to a bestperforming access terminal of the population of access terminals isupdated to a different pilot sequence that reduces performance of thebest performing access terminal.

In one embodiment, the step of updating the first pilot sequenceassigned to the worst performing access terminal is performediteratively until one or more criteria are satisfied. The one or morecriteria may include performance of the worst performing access terminalimproves by less than a threshold amount. In one embodiment, the step ofupdating the first pilot sequence assigned to the worst performingaccess terminal and the step of updating the second pilot sequenceassigned to the best performing access terminal are performediteratively until at least one of: performance of each of the populationof access terminals is within a threshold performance amount of eachother, and a predetermined number of iterations is satisfied.

In one embodiment, at least some of the pilot sequences arenon-orthogonal.

In one embodiment, the performance of the population of access terminalsis based on a signal-to-noise ratio of each of the population of accessterminals.

In one embodiment, assigning pilot sequences to a population of accessterminals includes randomly assigning pilot sequences to the populationof access terminals.

In one embodiment, the population of access terminals communicate with aplurality of access points based on time division duplex protocols.

These and other advantages of the invention will be apparent to those ofordinary skill in the art by reference to the following detaileddescription and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a high-level overview of a distributed cell-free wirelesscommunications system;

FIG. 2 shows a communications systems operating in accordance with timedivision duplex communication protocols;

FIG. 3 shows a system for assigning pilots to a population of accessterminals;

FIG. 4 shows a method for assigning pilots to a population of accessterminals; and

FIG. 5 shows a high-level block diagram of a computer for assigningpilots to a population of access terminals.

DETAILED DESCRIPTION

FIG. 1 shows a high-level overview of a distributed cell-free wirelesscommunications system 100, in accordance with one or more embodiments.Communications system 100 includes a select population of M serviceantennas or access points 102-a, 102-b, 102-c, 102-d, 102-e, 102-f, . .. , 102-M (collectively referred to as access points 102), whichsimultaneously serve Kuser access terminals 104-a, 104-b, 104-c, 104-d,. . . , 104-K (collectively referred to as access terminals 104). Accesspoints 102 are connected to each other and to hub node 106 over backhaulnetwork 108. While backhaul network 108 may typically be a fixed,landline network, such as, e.g., a fiber optic network, it should beunderstood that backhaul network 108 may be any suitable communicationsnetwork. For example, backhaul network 108 may be a wireless network. Insome embodiments, a designated subpopulation of access terminals 104 mayalso assume the role of access points 102. Access terminals 104 may havecapacity reserved for performing in such a dual role.

Each access point 102 and access terminal 104 is equipped with anantenna element and is randomly located over a large geographical area,such as, e.g., a city. Although access points 102 and access terminals104 are shown, and discussed herein, as comprising a single antennaelement, other embodiments are possible in which some or all of theaccess points 102 include multi-element arrays. It should be understoodthat the principles discussed herein may be readily extended to suchother embodiments.

Communications system 100 may include any number of access points 102and access terminals 104. However, in one embodiment, the total number Mof access points 102 is much larger than the total number K of accessterminals 104, such that M>>K>>1. For example, the total number ofaccess points 102 may be larger than the total number of accessterminals 104 by a factor of two or more, or even by a factor of ten ormore. The minimum distance between access points 102 is preferablygreater than one-fourth the operating wavelength so as to avoid strongcorrelations in the channel coefficients of neighboring access points.The principles discussed herein may be performed without reliance on acellular structure or cellular boundaries, although the population ofaccess points 102 may have other modes of operation in which it isorganized into cells.

As shown in FIG. 1, each access point 102 has a respective propagationchannel 110-a, 110-b, 110-c, 110-d, 110-e, 110-f, . . . , 110-M(collectively referred to as propagation channels 110) to accessterminal 104-a that it serves. While FIG. 1 shows propagation channel110 between each access point 102 and access terminal 104-a, it shouldbe understood that each access point 102 has a propagation channel toeach access terminal 104. To simplify the figures, propagation channelsbetween other access points 102 and other access terminals 104 have beenomitted for clarity.

In one embodiment, the transmission from access points 102 to accessterminals 104 (i.e., downlink transmission) and the transmission fromaccess terminals 104 to access points 102 (i.e., uplink transmission)proceed following time division duplex (TDD) communication protocols. Inaccordance with TDD communication protocols, the downlink and uplinkchannels are separated in time but use the same frequencies. Byreciprocity then, the channel estimates for each downlink channel may betaken as equal to the estimates for the corresponding uplink channel.Any channel estimate will be valid only within a coherence interval. Thecoherence interval depends on the fading characteristics of theparticular network of interest. In typical mobile networks, thecoherence interval is approximately the time for a mobile terminal totravel a distance of one-fourth the operating wavelength.

FIG. 2 shows communication system 200 operating in accordance with TDDcommunication protocols, in accordance with one or more embodiments. AllK access terminals 104 in an active subpopulation of access terminalssynchronously and simultaneously transmit their uplink signals to all Maccess points 102 in an active subpopulation of access points over theirrespective propagation channel 202-a, 202-b, 202-c, 202-d, . . . , 202-K(collectively referred to as propagation channels 202). All K accessterminals 104 synchronously and simultaneously send pilot sequencesφ_(j) to all M access points 102 over their respective propagationchannel 202, where j=1, . . . , K. Note that some pilot sequences can bereused (i.e., for some j and K, it could be the case that φ_(j)=φ_(k)).The transmission of uplink signals and pilot sequences are shown in FIG.2, and discussed herein, from access terminals 104 to a selected accesspoint 102-a. It should also be understood that each of the accessterminals 104 also simultaneously transmit their uplink signals andpilot sequences to all other access points 102.

Accordingly, a complex-valued channel coefficient g_(ij) is definedbetween each access point 102 and access terminal 104-a. Antenna i ofaccess point 102-a estimates the channel coefficient g_(ij) to provideestimated channel coefficient ĝ_(ij) where j=1, . . . , K. Access point104-a uses the estimated channel coefficient ĝ_(ij) to decode the uplinksignals that were previously sent by the access terminals 104. Accesspoint 104-a also uses the estimated channel coefficient ĝ_(ij) to form asignal x_(i) that comprises the data intended for all K access terminals104.

Such communication in accordance with TDD communication protocols may beperformed using the method described in U.S. patent application Ser. No.13/238,329, entitled “System and Method of Wireless Communication usingLarge-Scale Antenna Networks,” which is incorporated herein by referencein its entirety.

High throughput in communication system 200 may be achieved due to theestimated channel coefficient ĝ_(ij). The best estimated channelcoefficient ĝ_(ij) can be obtained if the pilots φ_(j) are orthogonal(i.e., φ_(j)*φ_(k)=0). However, when the number of K access terminals104 is large, orthogonal pilots φ_(j) are not able to be used.Specifically, as the number of access terminals increases, the length ofthe pilot sequences would have to increase to maintain orthogonality(i.e., pilot sequences would consist of at least K elements each). Inother words, the pilots would be t-tuples, with t≧K. Therefore, if K islarge, the time required for long pilot sequences may be too long due tothe limited length of the coherence interval. Thus, where the number ofK access terminals is large, short, non-orthogonal pilots are assignedto the access terminals 104. With high probability, two access terminalsthat are in close vicinity of each other will use the same pilotsequence. As a result, the performance of these access terminals willsuffer due to high pilot contamination.

FIG. 3 shows a system 300 for assigning pilots, in accordance with oneor more embodiments. System 300 assigns pilots that are relatively shortand therefore non-orthogonal in accordance with an iterative greedymanner such that a high level of system performance is maintained closeto the ideal case where all pilots are orthogonal.

Hub node 106 comprises a scheduler 306 for assigning pilots betweenaccess terminals 104 and access point 102-a in a greedy iterativemanner. It should be understood that scheduler 306 in hub node 106 mayalso assign pilots between access terminals 104 and other access points102. For a select active subpopulation of access terminals 104,scheduler 306 assigns pilot sequences to each access terminal 104.Preferably, the pilot sequences are assigned randomly to each accessterminal 104. In one embodiment, at least some of the randomly assignedpilot sequences are non-orthogonal. Identifying indices of the randomlyassigned pilot sequences are forwarded to access point 102-a viabackhaul network 108. Access point 102-a transmits the identifyingindices to access terminals 104.

Scheduler 306 evaluates the performance of the access terminals 104using the randomly assigned pilot sequences. For example, in oneembodiment, the performance of access terminals 104 may be based uponits pilot contamination measured using a signal-to-noise ratio (SNR). Inanother embodiment, the performance of access terminals 104 may be basedupon its pilot contamination evaluated from a calculated SNR. Scheduler306 identifies a worst performing access terminal (e.g., an accessterminal with a lowest SNR) and assigns to it a different pilot sequencethat improves performance of the worst performing access terminal.Indices identifying the updated assignment of pilot sequences aretransmitted to access point 102-a and access terminals 104 and theperformance of access terminals 104 are again evaluated. In oneembodiment, scheduler 306 iteratively determines a worst performingaccess terminal and assigns to it a different pilot sequence thatimproves its performance. The worst performing access terminal at eachiteration may be the same or different access terminal from the previousiteration. The pilot sequences of the worst performing access terminalsare iteratively updated with a pilot sequence that improves itsperformance until one or more criteria are satisfied. For example, theone or more criteria may be that performance of a worst performingaccess terminal improves by less than a threshold amount. In oneembodiment, the threshold amount may include no improvement in theperformance of the worst performing access terminal.

Scheduler 306 then evaluates the performance of the access terminals 104and identifies a best performing access terminal. For example, the bestperforming access terminal may be determined based on its SNR (e.g., anaccess terminal with a highest SNR). Scheduler 306 assigns to the bestperforming access terminal a different pilot sequence that reduces itsperformance.

In one embodiment, scheduler 306 returns to iteratively update pilotsequences of the worst performing access terminals to different pilotsequences that improve their performance until the one or more criteriais satisfied, then updates a pilot sequence of the best performingaccess terminal to a different pilot sequence that reduces itsperformance. Scheduler 306 may iteratively repeat this process until,e.g., all access terminals 104 have similar performance (e.g., theirSNRs are within a threshold amount of each other) and/or a predeterminednumber of iterations is reached.

Based on the pilot sequences assigned according to the iterative greedymanner discussed herein, access point 102-a determines estimated channelcoefficients ĝ_(ij), in accordance with TDD communication protocols asdiscussed above. Access point 102-a includes a co-located processingdevice 302 and memory device 304 for storing the estimated channelcoefficients ĝ_(ij) obtained from the assigned pilot signals.

Advantageously, the iteratively greedy pilot assignment of scheduler 306assigns pilot sequences between access terminals and access points thatresults in an improved estimated channel coefficient ĝ_(ij). Theiteratively greedy pilot assignment has been found to improveperformance over existing solutions.

FIG. 4 shows a method 400 for assigning pilots, in accordance with oneor more embodiments. At step 402, pilot sequences are assigned to aselect population of access terminals. The pilot sequences may beassigned randomly to the population of access terminals. In oneembodiment, at least some of the pilot sequences are non-orthogonalpilot sequences. The population of access terminals may communicate witha plurality of access points based on TDD communication protocols. Atstep 404, performance of each of the population of access terminals isevaluated using their assigned pilot sequences. The performance of thepopulation of access terminals may be evaluated, e.g., based upon itspilot contamination using the SNR of each access terminal.

At step 406, a first pilot sequence assigned to a worst performingaccess terminal of the population of access terminals is updated to adifferent pilot sequence that improves performance of the worstperforming access terminal. For example, the worst performing accessterminal may be the access terminal with a lowest SNR. At step 408, itis determined whether performance of the worst performing accessterminal improved by less than a threshold amount. For example, thethreshold amount may include no improvement in the performance of theworst performing access terminal. If performance of the worst performingaccess terminal does not improve by less than a threshold amount, method400 returns to step 406. Step 406 is iterated until performance of theworst performing access terminal does improve by less than a thresholdamount, and then proceeds to step 410. In one embodiment, steps 406 and408 may additionally or alternatively be iterated for a predeterminednumber of iterations.

At step 410, a second pilot sequence assigned to a best performingaccess terminal of the population of access terminals is updated to adifferent pilot sequence that reduces performance of the best performingaccess terminal. For example, the best performing access terminal may bethe access terminal with a highest SNR.

At step 412, it is determined whether one or more stopping criteria aresatisfied. For example, the one or more stopping criteria may includewhether the performance of each of the population of access terminals iswithin a threshold performance amount of each other. For example, it isdetermined whether the SNRs of each of the population of accessterminals are within a threshold performance amount of each other. Theone or more stopping criteria may also include whether the number ofiterations (of steps 406-412) satisfies a predetermined number ofiterations. Other stopping criteria are also contemplated. In oneembodiment, if the one or more stopping criteria are not satisfied,method 400 returns to step 406 and steps 406, 408, 410, and 412 areiterated until the one or more stopping criteria are satisfied. Once theone or more stopping criteria are satisfied, method 400 ends at step414. In some embodiments, method 400 may repeat for a new selectpopulation of access terminals.

Systems, apparatuses, and methods described herein may be implementedusing digital circuitry, or using one or more computers using well-knowncomputer processors, memory units, storage devices, computer software,and other components. Typically, a computer includes a processor forexecuting instructions and one or more memories for storing instructionsand data. A computer may also include, or be coupled to, one or moremass storage devices, such as one or more magnetic disks, internal harddisks and removable disks, magneto-optical disks, optical disks, etc.

Systems, apparatus, and methods described herein may be implementedusing computers operating in a client-server relationship. Typically, insuch a system, the client computers are located remotely from the servercomputer and interact via a network. The client-server relationship maybe defined and controlled by computer programs running on the respectiveclient and server computers.

Systems, apparatus, and methods described herein may be implementedwithin a network-based cloud computing system. In such a network-basedcloud computing system, a server or another processor that is connectedto a network communicates with one or more client computers via anetwork. A client computer may communicate with the server via a networkbrowser application residing and operating on the client computer, forexample. A client computer may store data on the server and access thedata via the network. A client computer may transmit requests for data,or requests for online services, to the server via the network. Theserver may perform requested services and provide data to the clientcomputer(s). The server may also transmit data adapted to cause a clientcomputer to perform a specified function, e.g., to perform acalculation, to display specified data on a screen, etc. For example,the server may transmit a request adapted to cause a client computer toperform one or more of the method steps described herein, including oneor more of the steps of FIG. 4. Certain steps of the methods describedherein, including one or more of the steps of FIG. 4, may be performedby a server or by another processor in a network-based cloud-computingsystem. Certain steps of the methods described herein, including one ormore of the steps of FIG. 4, may be performed by a client computer in anetwork-based cloud computing system. The steps of the methods describedherein, including one or more of the steps of FIG. 4, may be performedby a server and/or by a client computer in a network-based cloudcomputing system, in any combination.

Systems, apparatus, and methods described herein may be implementedusing a computer program product tangibly embodied in an informationcarrier, e.g., in a non-transitory machine-readable storage device, forexecution by a programmable processor; and the method steps describedherein, including one or more of the steps of FIG. 4, may be implementedusing one or more computer programs that are executable by such aprocessor. A computer program is a set of computer program instructionsthat can be used, directly or indirectly, in a computer to perform acertain activity or bring about a certain result. A computer program canbe written in any form of programming language, including compiled orinterpreted languages, and it can be deployed in any form, including asa stand-alone program or as a module, component, subroutine, or otherunit suitable for use in a computing environment.

A high-level block diagram 500 of an example computer that may be usedto implement systems, apparatus, and methods described herein isdepicted in FIG. 5. Computer 502 includes a processor 504 operativelycoupled to a data storage device 512 and a memory 510. Processor 504controls the overall operation of computer 502 by executing computerprogram instructions that define such operations. The computer programinstructions may be stored in data storage device 512, or other computerreadable medium, and loaded into memory 510 when execution of thecomputer program instructions is desired. Thus, the method steps of FIG.4 can be defined by the computer program instructions stored in memory510 and/or data storage device 512 and controlled by processor 504executing the computer program instructions. For example, the computerprogram instructions can be implemented as computer executable codeprogrammed by one skilled in the art to perform the method steps of FIG.4. Accordingly, by executing the computer program instructions, theprocessor 504 executes the method steps of FIG. 4. Computer 502 may alsoinclude one or more network interfaces 506 for communicating with otherdevices via a network. Computer 502 may also include one or moreinput/output devices 508 that enable user interaction with computer 502(e.g., display, keyboard, mouse, speakers, buttons, etc.).

Processor 504 may include both general and special purposemicroprocessors, and may be the sole processor or one of multipleprocessors of computer 502. Processor 504 may include one or morecentral processing units (CPUs), for example. Processor 504, datastorage device 512, and/or memory 510 may include, be supplemented by,or incorporated in, one or more application-specific integrated circuits(ASICs) and/or one or more field programmable gate arrays (FPGAs).

Data storage device 512 and memory 510 each include a tangiblenon-transitory computer readable storage medium. Data storage device512, and memory 510, may each include high-speed random access memory,such as dynamic random access memory (DRAM), static random access memory(SRAM), double data rate synchronous dynamic random access memory (DDRRAM), or other random access solid state memory devices, and may includenon-volatile memory, such as one or more magnetic disk storage devicessuch as internal hard disks and removable disks, magneto-optical diskstorage devices, optical disk storage devices, flash memory devices,semiconductor memory devices, such as erasable programmable read-onlymemory (EPROM), electrically erasable programmable read-only memory(EEPROM), compact disc read-only memory (CD-ROM), digital versatile discread-only memory (DVD-ROM) disks, or other non-volatile solid statestorage devices.

Input/output devices 508 may include peripherals, such as a printer,scanner, display screen, etc. For example, input/output devices 508 mayinclude a display device such as a cathode ray tube (CRT) or liquidcrystal display (LCD) monitor for displaying information to the user, akeyboard, and a pointing device such as a mouse or a trackball by whichthe user can provide input to computer 502.

Any or all of the systems and apparatus discussed herein, includingelements of system 100 of FIG. 1, system 200 of FIG. 2, and system 300of FIG. 3, such as, e.g., scheduler 306 of FIG. 3, may be implementedusing one or more computers such as computer 502.

One skilled in the art will recognize that an implementation of anactual computer or computer system may have other structures and maycontain other components as well, and that FIG. 5 is a high levelrepresentation of some of the components of such a computer forillustrative purposes.

The foregoing Detailed Description is to be understood as being in everyrespect illustrative and exemplary, but not restrictive, and the scopeof the invention disclosed herein is not to be determined from theDetailed Description, but rather from the claims as interpretedaccording to the full breadth permitted by the patent laws. It is to beunderstood that the embodiments shown and described herein are onlyillustrative of the principles of the present invention and that variousmodifications may be implemented by those skilled in the art withoutdeparting from the scope and spirit of the invention. Those skilled inthe art could implement various other feature combinations withoutdeparting from the scope and spirit of the invention.

The invention claimed is:
 1. A method for assigning pilot sequences,comprising: assigning pilot sequences to a population of accessterminals; updating a first pilot sequence assigned to a worstperforming access terminal of the population of access terminals to adifferent pilot sequence that improves performance of the worstperforming access terminal; and updating a second pilot sequenceassigned to a best performing access terminal of the population ofaccess terminals to a different pilot sequence that reduces performanceof the best performing access terminal.
 2. The method as recited inclaim 1, wherein the step of updating the first pilot sequence assignedto the worst performing access terminal is performed iteratively untilone or more criteria are satisfied.
 3. The method as recited in claim 2,wherein the one or more criteria comprises: performance of the worstperforming access terminal improves by less than a threshold amount. 4.The method as recited in claim 1, wherein the step of updating the firstpilot sequence assigned to the worst performing access terminal and thestep of updating the second pilot sequence assigned to the bestperforming access terminal are performed iteratively until at least oneof: performance of each of the population of access terminals is withina threshold performance amount of each other; and a predetermined numberof iterations is satisfied.
 5. The method as recited in claim 1, whereinat least some of the pilot sequences are non-orthogonal.
 6. The methodas recited in claim 1, wherein performance of the population of accessterminals is based on a signal-to-noise ratio of each of the populationof access terminals.
 7. The method as recited in claim 1, whereinassigning pilot sequences to the population of access terminalscomprises randomly assigning pilot sequences to the population of accessterminals.
 8. The method as recited in claim 1, wherein the populationof access terminals communicate with a plurality of access points basedon time division duplex protocols.
 9. A computer readable medium storingcomputer program instructions for assigning pilot sequences, which, whenexecuted on a processor, cause the processor to perform operationscomprising: assigning pilot sequences to a population of accessterminals; updating a first pilot sequence assigned to a worstperforming access terminal of the population of access terminals to adifferent pilot sequence that improves performance of the worstperforming access terminal; and updating a second pilot sequenceassigned to a best performing access terminal of the population ofaccess terminals to a different pilot sequence that reduces performanceof the best performing access terminal.
 10. The computer readable mediumas recited in claim 9, wherein the operation of updating the first pilotsequence assigned to the worst performing access terminal is performediteratively until one or more criteria are satisfied.
 11. The computerreadable medium as recited in claim 10, wherein the one or more criteriacomprises: performance of the worst performing access terminal improvesby less than a threshold amount.
 12. The computer readable medium asrecited in claim 9, wherein the operation of updating the first pilotsequence assigned to the worst performing access terminal and theoperation of updating the second pilot sequence assigned to the bestperforming access terminal are performed iteratively until at least oneof: performance of each of the population of access terminals is withina threshold performance amount of each other; and a predetermined numberof iterations is satisfied.
 13. The computer readable medium as recitedin claim 9, wherein at least some of the pilot sequences arenon-orthogonal.
 14. The computer readable medium as recited in claim 9,wherein performance of the population of access terminals is based on asignal-to-noise ratio of each of the population of access terminals. 15.The computer readable medium as recited in claim 9, wherein assigningpilot sequences to the population of access terminals comprises randomlyassigning pilot sequences to the population of access terminals.
 16. Anapparatus for assigning pilot sequences, comprising: a processor; and amemory to store computer program instructions, the computer programinstructions when executed on the processor cause the processor toperform operations comprising: assigning pilot sequences to a populationof access terminals; updating a first pilot sequence assigned to a worstperforming access terminal of the population of access terminals to adifferent pilot sequence that improves performance of the worstperforming access terminal; and updating a second pilot sequenceassigned to a best performing access terminal of the population ofaccess terminals to a different pilot sequence that reduces performanceof the best performing access terminal.
 17. The apparatus as recited inclaim 16, wherein the operation of updating the first pilot sequenceassigned to the worst performing access terminal is performediteratively until one or more criteria are satisfied.
 18. The apparatusas recited in claim 16, wherein the operation of updating the firstpilot sequence assigned to the worst performing access terminal and theoperation of updating the second pilot sequence assigned to the bestperforming access terminal are performed iteratively until at least oneof: performance of each of the population of access terminals is withina threshold performance amount of each other; and a predetermined numberof iterations is satisfied.
 19. The apparatus as recited in claim 16,wherein at least some of the pilot sequences are non-orthogonal.
 20. Theapparatus as recited in claim 16, wherein performance of the populationof access terminals is based on a signal-to-noise ratio of each of thepopulation of access terminals.